Aug30-11, 06:44 PM
Im working on understanding Gröbner bases. I've understood how to show existance and uniqueness(of reduced Gröbner bases).
To understand how to actually compute them, I need to understand Syzygies in free modules.
The theorem reads thus:
In a ring of multivariate polynomials over a field, if S =(s_1,s_2,s_3...s_n) is a syzygy of (m_1,m_2,m_3...m_n), where every m_i is a monomial, S is a linear combination of the canonical pair-wise Syzygies.
I've been trying to get some headway on this proof for a week now, with little success.
Any comments or hints appreciated! Thank you!
|Register to reply|
|Linear Transformation to Block-wise Stack Matrix||Linear & Abstract Algebra||11|
|Random variables that are triple-wise independent but quadruple-wise dependent||Set Theory, Logic, Probability, Statistics||2|
|Piece-wise linear diode model||Electrical Engineering||6|
|What is a linear combination?||Calculus & Beyond Homework||1|
|linear algebra-linear combination||Calculus & Beyond Homework||2|